Parallel matrix multiplication on a linear array with a reconfigurable pipelined bus system

The known fast sequential algorithms for multiplying two N×N matrices (over an arbitrary ring) have time complexity O(N^α ), where 2<α<3. The current best value of α is less than 2.3755. We show that, for all 1⩽p⩽N^α, multiplying two N×N matrices can be performed on a p-processor linear array with a reconfigurable pipelined bus system (LARPBS) in O(N _m/P+(N²/p²α/)log p) time. This is currently the fastest parallelization of the best known sequential matrix multiplication algorithm on a distributed memory parallel system. In particular, for all 1⩽p⩽N^2.3755, multiplying two N×N matrices can be performed on a p-processor LARPBS in O(N^2.3755/p+(N²)/p^0.8419log p) time and linear speedup can be achieved for p as large as O(N^2.3755/(log N)^6.3262). Furthermore, multiplying two N×N matrices can be performed on an LARPBS with O(N^α) processors in O(log N) time. This compares favorably with the performance on a PRAM